Problem: The sum of two numbers is $52$, and their difference is $2$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 52}$ ${x-y = 2}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 54 $ $ x = \dfrac{54}{2} $ ${x = 27}$ Now that you know ${x = 27}$ , plug it back into $ {x+y = 52}$ to find $y$ ${(27)}{ + y = 52}$ ${y = 25}$ You can also plug ${x = 27}$ into $ {x-y = 2}$ and get the same answer for $y$ ${(27)}{ - y = 2}$ ${y = 25}$ Therefore, the larger number is $27$, and the smaller number is $25$.